Mathematics on the Crossroad of Centuries

Explore advanced mathematical research through this conference featuring 19 lectures delivered by leading mathematicians in honor of Maxim Kontsevich's 60th birthday. Delve into cutting-edge topics spanning algebra, combinatorics, topology, algebraic geometry, and theoretical physics, examining the profound connections between mathematics and physics at the intersection of the 20th and 21st centuries. Discover groundbreaking work in homological mirror symmetry, quantum link invariants, geometric quantization, symplectic geometry, Calabi-Yau threefolds, modular forms, spectral mirror symmetry, Donaldson-Thomas invariants, and Hodge theory. Learn from distinguished speakers including Alexander Goncharov on exponential volumes, Mina Aganagic on mirror symmetry, Lauren Williams on the amplituhedron, Denis Auroux on SYZ mirror symmetry, Don Zagier on modular forms and differential equations, and Curtis McMullen on billiards and arithmetic, among others. Gain insights into motivic invariants, birational geometry, noncommutative structures, and the geometric aspects of representation theory through presentations that showcase the spectacular interdisciplinary nature of contemporary mathematical research.

Syllabus

Alexander Goncharov - Exponential Volumes in Geometry and Representation Theory
Mina Aganagic - Homological Mirror Symmetry and Quantum Link Invariants
Yan Soibelman - Motivic Invariants of Moduli of Irregular Parabolic Higgs Bundles and Bundles (...)
Tony Pantev - Birational and Singularity Invariants from nc Hodge Theory
Jorgen Andersen - Geometric Quantization of General Kahler Manifolds
Lauren Williams - Combinatorics and Geometry of the Amplituhedron
Kenji Fukaya - $A$ Infinity Functor in Symplectic Geometry and Gauge Theory
John Pardon - Universally Counting Curves in Calabi-Yau Threefolds
Denis Auroux - An Update on SYZ Mirror Symmetry and Family Floer Theory
Davide Gaiotto - Holomorphic-Topological Twists and their Applications
Don Zagier - Modular Forms and Differential Equations
Mohammed Abouzaid - Prospects for Spectral Mirror Symmetry
Yuri Tschinkel - Moduli Spaces of Points on the Projective Line and Other Varieties with Many (...)
Pavel Etingof - Periodic pencils of flat connections and their $p$-curvature
Vladimir Drinfeld - Shimurian analogs of Barsotti-Tate groups.
Tom Bridgeland - Geometry from Donaldson-Thomas Invariants
Alexander Odesskii - Noncommutative Elliptic Poisson Structures on Projective Spaces
Fabian Haiden - Counting in Calabi-Yau Categories
Curtis McMullen - Billiards, Arithmetic and Hodge Theory